Special form of Gompertz model and its application

Samba S.R. Pasupuleti, Prasanta Pathak

Abstract

In this paper, we have proposed a special form of Gompertz model in which all parameters have direct demographic interpretation. The new model does not differ in structure from the classical Gompertz model. However, it has been shown to be more useful in various instances. For example, when quantifying fertility behaviour, this model adds a dimension called the effective fertility period, defined as the age interval within which the fertility level of a cohort rises from 5% to 95% of its saturation level or the Cohort Total Fertility Rate. Relative merits and demerits of the proposed model, in comparison to the other popular forms and the transformed versions of the Gompertz model, are discussed. The proposed model has been fitted to the cohort fertility schedules of high fertility countries like India and low fertility countries such as the USA, Austria, Slovakia, etc. In the context of India, the proposed model has been compared with other fertility models like Gamma model, Beta model, Hadwiger model, CT model, etc. It was found that the proposed model provides good fit to the cohort fertility schedules of high and low fertility countries.